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Recent Developments in the Probabilistic Analysis of the Simplex Algorithm

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Operations Research Proceedings 1994

Part of the book series: Operations Research Proceedings ((ORP,volume 1994))

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Summary

The article provides an asymptotic probabilistic analysis of the variance of the number of pivot steps required by phase II of the “shadow vertex algorithm” — a parametric variant of the simplex algorithm. The analysis is done for data that satisfy a spherically symmetric distribution law in the n-dimensional unit ball.

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References

  1. Borgwardt, K. H.: The Simplex Method—A Probabilistic Analysis. Springer, New York, Berlin, Heidelberg (1987)

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  2. Borgwardt, K. H.: Verschärfung des Polynomialitätsbeweises für die erwartete Anzahl von Schattenecken im Rotationssymmetrie-Modell. Shaker, Aachen (1994)

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  3. Feller, W.: An Introduction to Probability and its Applications, Vol I–II. Wiley, New York ( 1960, 1966 )

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  4. Küfer, K.-H.: On the Variance of the Number of Pivot Steps Required by the Simplex Algorithm. To appear in ZOR

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  5. Shamir, R.: The Efficiency of the Simplex Method: A Survey. Management Science 33 (1987) 241–262

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© 1995 Springer-Verlag Berlin Heidelberg

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Küfer, KH. (1995). Recent Developments in the Probabilistic Analysis of the Simplex Algorithm. In: Derigs, U., Bachem, A., Drexl, A. (eds) Operations Research Proceedings 1994. Operations Research Proceedings, vol 1994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79459-9_2

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  • DOI: https://doi.org/10.1007/978-3-642-79459-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58793-4

  • Online ISBN: 978-3-642-79459-9

  • eBook Packages: Springer Book Archive

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